Note that [1]}, [2]} have studied T-E inequalities for the case of stable LDS. However, a framework to provide exponential concentration inequalities for deviation of empirical averages of some unbounded test function is missing. Concentration for nonlinear random dynamical systems is not well explored, partly because they are not necessarily contractive in trivial metric.
As shown in the following sections, we circumvent this issue by using a contractive metrics introduced by [3]} at the loss of uniform transportation-entropy constant. However, we still manage to provide sharp concentration inequalities by directly linking strong contractions offered by exponential Lyapunov function to transportation-entropy constant, using results from [4]}.
